Details

Time bar (total: 9.3s)

sample89.0ms

Algorithm
intervals
Results
19.0ms375×body80nan
17.0ms33×body1280valid
9.0ms167×body80valid
6.0ms28×body640valid
5.0ms21×body1280nan
3.0ms14×body640nan
2.0ms16×body320nan
2.0ms12×body320valid
2.0ms16×body160valid
1.0ms7×body160nan

simplify87.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
14.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
23.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
12.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
29.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
441.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms
(* (sqrt 2.0) t)
225.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify62.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04171207
120511099
250021094

prune315.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.7b

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.9b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.0ms
(/ (pow l 2) x)
4.0ms
(/ (pow t 2) x)
9.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
172.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261067
12113984
25001978

prune463.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
77×times-frac
56×unpow-prod-down
46×add-cube-cbrt *-un-lft-identity
37×associate-*r*
35×add-exp-log
24×unswap-sqr
22×cbrt-prod
18×sqr-pow
12×div-exp prod-exp
11×add-cbrt-cube unpow2
10×associate-*l*
9×associate-*r/
8×pow-to-exp pow-exp associate-/l*
6×add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×associate-/r* sqrt-prod
2×cbrt-undiv associate-+r+ cbrt-unprod div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num sum-log *-commutative
Counts
4 → 175
Calls
4 calls:
28.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
4.0ms
(/ (pow t 2) x)
9.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

series356.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
92.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
19.0ms
(/ (pow t 2) x)
194.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

simplify106.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
08512019
142561786
250011699

prune705.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))))))
3.9b
(/ (pow (cbrt l) 4) (cbrt x))
9.7b
(/ (pow t 2) x)
27.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x)))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
66×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
54×cbrt-prod unpow-prod-down
18×associate-/l*
14×add-exp-log
11×sqr-pow
9×associate-/r*
8×associate-*r/
7×add-cbrt-cube
6×div-exp add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+ unpow2
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 171
Calls
4 calls:
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))))))
7.0ms
(/ (pow (cbrt l) 4) (cbrt x))
4.0ms
(/ (pow t 2) x)
9.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x)))))))

series498.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x))))))
97.0ms
(/ (pow (cbrt l) 4) (cbrt x))
19.0ms
(/ (pow t 2) x)
269.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (* (/ (pow (cbrt l) 4) (cbrt x)) (/ (fabs (cbrt l)) (cbrt x))) (/ (sqrt (pow (cbrt l) 2)) (cbrt x)))))))

simplify99.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07682505
132112384
250022312

prune908.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes574.0ms

Accuracy

73.1% (6.4b remaining)

Error of 10.3b against oracle of 3.9b and baseline of 27.7b

bsearch420.0ms

Steps
ItersRangePoint
10
3.953010055594803e+65
5.675578072705738e+76
5.6231609413745994e+76
4
-7.071793886822642e-265
-4.409591838871608e-265
-6.971334801643659e-265
7
-6.112379719888229e-117
-7.277680353313571e-119
-7.40273667700519e-119
7
-6.795528143553319e+48
-1.0864178206604457e+47
-6.113526319583239e+48

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079127
181127
281127

end0.0ms

sample2.1s

Algorithm
intervals
Results
484.0ms9913×body80nan
263.0ms5098×body80valid
210.0ms828×body1280valid
208.0ms1032×body640valid
142.0ms581×body1280nan
116.0ms614×body640nan
98.0ms666×body320valid
51.0ms350×body320nan
38.0ms376×body160valid
17.0ms178×body160nan